# An equation for a time-dependent profit rate

## TL;DR

This paper derives a time-dependent profit rate equation based on a labor theory of value without assuming equilibrium, linking profit rate to productivity, labor force growth, and surplus value ratios, with an empirical test proposed.

## Contribution

It introduces a novel equation for the profit rate over time derived from a labor theory of value without equilibrium assumptions.

## Key findings

- Profit rate depends on retarded averages of productivity and labor force growth.
- Profit rate is proportional to the ratio of current surplus value to its retarded average.
- An empirical test for the derived profit rate equation is suggested.

## Abstract

Taking as a hypothesis a form of the labour theory of value, and $without$ $assuming$ $equilibrium$, we derive an equation that yields the profit-rate $\pi$ as a function of time. For a mature economy, $\pi(t)$ reduces to the product of two factors: ($i$) a certain $retarded$ $average$ of the sum of the growth-rates of productivity and of the size of the labour-force measured by hours worked, and ($ii$) the ratio of the current rate of surplus value to its own retarded average. We also suggest an empirical test of the equation.